Pyramid pattern

Pyramid pattern

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about making patterns and finding a rule.
Your teacher will show you how to make a pyramid pattern.
 
 

Y    N
a)
 
Firstly, make the next size pyramid up.
 
b)
 
Now make the next size pyramid up.
 
c)
Altogether how many triangles did you need to make the last pyramid pattern? __________
 
d)
i)
  
 

ii)
How many triangles would you need to make the next size up from this pyramid pattern?
 
__________
  
How did you work this out?
 
 
 
 
 
 
 
Task administration: 
This task is completed with pen and paper, and other equipment.
 
Equipment:
Sets of same-sized triangles (e.g., attribute shapes, construction pieces, e.g., Jovo).
  • This task assesses a student's ability to build up pyramid patterns using triangles and predict the number of triangles needed for the next pattern.
  • This task can be carried out by reading the instructions to students one at a time and/or giving them the instructions to read.
  • You can either use the checkboxes on the instruction sheet or the separate teacher checklist to monitor the students as they make the pyramids.
  • Demonstrate the construction of the first two layers of the pyramid pattern to the students as shown below.
  • Make the correct pyramid shape for the students if it has been made incorrectly.

Teacher instructions:
I want you to make pyramid patterns using these triangles.
This is the smallest pyramid. [Place 1 triangle on the table.]

This is the next size up. [Make a 4 triangle pyramid.]

 

 

Level:
3
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, recursive rules, model construction, quadratic equation
Description of task: 
In this practical task, students construct pyramid patterns using triangles. They then predict how many triangles would be needed for the next size pyramid and explain their rule.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
a)  

b)  
c)   16
d) i)
ii)		 25 (or answer to c) + 9)
Add on a row of 9 triangles to the last pyramid.
[Accept similar statement that shows an understanding of the pattern.]